Solve 2w^3/5div4w

$$\frac { 2 w ^ { 3 } } { 5 } \div 4 w$$

Evaluate

$$\frac{w^{4}}{10}$$

Solution Steps

Express \frac{\frac{2w^{3}}{5}}{4} as a single fraction.

$$\frac{2w^{3}}{5\times 4}w$$

Cancel out 2 in both numerator and denominator.

$$\frac{w^{3}}{2\times 5}w$$

Multiply 2 and 5 to get 10.

$$\frac{w^{3}}{10}w$$

Express \frac{w^{3}}{10}w as a single fraction.

$$\frac{w^{3}w}{10}$$

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$\frac{w^{4}}{10}$$

Differentiate w.r.t. w

$$\frac{2w^{3}}{5}$$

Steps Using Definition of a Derivative

Express \frac{\frac{2w^{3}}{5}}{4} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}w}(\frac{2w^{3}}{5\times 4}w)$$

Cancel out 2 in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}w}(\frac{w^{3}}{2\times 5}w)$$

Multiply 2 and 5 to get 10.

$$\frac{\mathrm{d}}{\mathrm{d}w}(\frac{w^{3}}{10}w)$$

Express \frac{w^{3}}{10}w as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}w}(\frac{w^{3}w}{10})$$

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}w}(\frac{w^{4}}{10})$$

The derivative of ax^{n} is nax^{n-1}.

$$4\times \frac{1}{10}w^{4-1}$$

Multiply 4 times \frac{1}{10}.

$$\frac{2}{5}w^{4-1}$$

Subtract 1 from 4.

$$\frac{2}{5}w^{3}$$